# Fungrim entry: 888581

$\mathrm{B}\!\left(a, b\right) = \frac{\Gamma(a) \Gamma(b)}{\Gamma\!\left(a + b\right)}$
Assumptions:$a \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \setminus \{0, -1, \ldots\}$
TeX:
\mathrm{B}\!\left(a, b\right) = \frac{\Gamma(a) \Gamma(b)}{\Gamma\!\left(a + b\right)}

a \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \setminus \{0, -1, \ldots\}
Definitions:
Fungrim symbol Notation Short description
BetaFunction$\mathrm{B}\!\left(a, b\right)$ Beta function
Gamma$\Gamma(z)$ Gamma function
CC$\mathbb{C}$ Complex numbers
ZZLessEqual$\mathbb{Z}_{\le n}$ Integers less than or equal to n
Source code for this entry:
Entry(ID("888581"),
Formula(Equal(BetaFunction(a, b), Div(Mul(Gamma(a), Gamma(b)), Gamma(Add(a, b))))),
Variables(a, b),
Assumptions(And(Element(a, SetMinus(CC, ZZLessEqual(0))), Element(b, SetMinus(CC, ZZLessEqual(0))))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-03-29 16:01:42.585089 UTC